Single- and coupled-channel radial inverse scattering with supersymmetric transformations

摘要: The present status of the three-dimensional inverse-scattering method with supersymmetric transformations is reviewed for coupled-channel case. We first revisit in a pedagogical way single-channel case, where approach shown to provide complete, efficient and elegant solution problem radial Schrodinger equation short-range interactions. A special emphasis put on differences between conservative non-conservative transformations, i.e. that do or not conserve behaviour solutions at origin. In particular, we show zero initial potential, transformation always equivalent pair transformations. These results are illustrated inversion neutron–proton triplet eigenphase shifts S- D-waves. then summarize extend our previous works systems coupled equations, stress remaining difficulties open questions this by putting it perspective mostly concentrate two-channel examples illustrate general principles while keeping mathematics as simple possible. discuss important difference equal-threshold different-threshold problems. For equal thresholds, can non-diagonal Jost scattering matrices. Iterations such case studied lead practical algorithms inversion. convenient particular technique mixing parameter be fitted without modifying eigenphases developed iterations pairs conjugate This applied S–D matrix, which exactly-solvable matrix potential models constructed. different seem able non-trivial coupling channels. contrast, single generate potentials starting from promising step towards full inverse threshold differences.